67.13.18 problem 20.1 (r)

Internal problem ID [16683]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.1 (r)
Date solved : Thursday, October 02, 2025 at 01:37:39 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=3*x^2*diff(diff(y(x),x),x)-7*x*diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{{1}/{3}}+c_2 \,x^{3} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

ode=3*x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^3+c_1 \sqrt [3]{x} \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*Derivative(y(x), (x, 2)) - 7*x*Derivative(y(x), x) + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sqrt [3]{x} + C_{2} x^{3} \]